Muon spin spectroscopy

Muon spin spectroscopy (µSR) is an experimental technique based on the implantation of spin polarized muons in matter and on the detection of the influence of the atomic, molecular or crystalline surroundings on their spin motion. The motion of the muon spin is due to the magnetic field experienced by the particle and may provide information on its local environment in a very similar way to other magnetic resonance techniques, such as Electron spin resonance (ESR or EPR) and, more closely, Nuclear magnetic resonance (NMR).

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Acronym

In analogy with the acronyms for these previously established spectroscopies, the muon spin spectroscopy is also known as µSR, which stands for Muon Spin Rotation, or Relaxation, or Resonance, depending respectively on whether the muon spin motion is predominantly a rotation (more precisely a precession around a still magnetic field), or a relaxation towards an equilibrium direction, or, again, a more complex dynamics dictated by the addition of short radio frequency pulses.

How it works

The time scale on which the spin motion may be exploited is that of the muon decay, i.e. a few mean lifetimes, each roughly 2.2 µs (2.2 millionths of a second). Both the production of muon beams with nearly perfect alignment of the spin to the beam direction (what was referred to above as spin polarization), and the ability to detect the muon spin direction at the instant of the muon decay rely on the violation of parity, which takes place whenever weak forces are at play.

In short this means that certain elementary events happen only when including clockwise (or only when including counterclockwise) rotations, For instance, the positive muon decays into a positron plus two neutrinos and the positron is preferentially emitted in the direction of the muon spin. therefore it would most often see the spin as a counterclockwise rotation while flying away from the decay point.

Spin alignment allows to produce a muon beam with aligned magnetic moments. We are able to inject muons into studying material and mouns serve as short-lived spies inside studying material [1]. Muons inside the crystal are able to send a message about the local magnetic field in their surroundings. After some time (half lifetime 2.2 µs) these spies decay and emit positrons. A beam of aligned muons produces asymmetric positron radiation. The asymmetry of positron radiation contains information about the direction of local magnetic field in the moment of muon decay. Taking into consideration the initial direction of muon magnetic moment and time interval between the moment of injection and moment of muon decay we can calculate the precesion frequency (how many times the muon magnetic moment turned around). The frequency of magnetic moment precesion depends on local magnetic field.

Since 1987 this method was used to mesure internal magnetic fields inside high-temperature superconductors [2]. High-temperature superconductors are Type II superconductors. In Type-II superconductors local magnetic fields inside the superconductor depend on the carrier density. Carrier density is one of the significant parameters of Bardeen-Cooper-Shrieffer [3] theory of superconductors.

Applications and Facilities

Muon Spin Rotation and Relaxation are mostly performed with positive muons. They are well suited to study magnetic fields at the atomic scale inside matter, such as those provided by the very different kinds of magnetic order and of superconducting states that are either encountered in some natural compounds or artificially produced by modern material science.

Another important field of application of µSR exploits the fact that positive muons behave chemically as light isotopes of the Hydrogen ion. This allows the investigation of the early stages of the formation of radicals in organic chemicals and in semiconductors.

µSR requires a particle accelerator for the production of a muon beam. This is presently achieved at few international large scale facilities in the world: The CMMS^[4] continuous source at TRIUMF^[5], Vancouver, Canada; The LMU^[6] continuous source at the Paul Scherrer Institut^[7], Villigen, Switzerland; The ISIS^[8] and the Riken-RAL^[9] pulsed sources at the Rutherford Appleton Laboratory^[10], Chilton, United Kingdom; the J-PARC^[11] facility, in Tokai, Japan, is completing a new pulsed source to replace that at KEK^[12]. Muan beam is available in Laboratory of Nuclear Problems, Joint Institute for Nuclear Research ^[13], Dubna, Russia. The International Society for µSR Spectroscopy (ISMS) exists to promote the worldwide advancement of µSR. Membership in the Society is open free of charge to all individuals in academia, government laboratories and industry who have an interest in the Society’s goals.

See also

• Muon
• Muonium
• Nuclear magnetic resonance

References

• ISIS Introductory course to µSR
• introduction to μSR
• µSR Brochure (a 3.2 MB PDF file)
• CMMS TRIUMF Center for Molecular and Materials Science